(CNN) -- Spain's Jorge Lorenzo has increased his overall lead in the world championship standings after victory in the French MotoGP at Le Mans -- the third race on the calendar.

The Yamaha rider started second on the grid behind world champion Valentino Rossi but, after briefly leading the race on lap seven, he eventually took control on the 10th lap to complete a six-second victory.

Teammate Rossi finished second with Honda's Andrea Dovizioso coming home in third position.

Lorenzo, who also won the second race of the season on his home track in Spain, leads the standings on 70 points -- nine points clear of Rossi.